The high-spin structure of the Z=76 nucleus Os-188 has been studied using the incomplete fusion reaction Li-7+W-186. A K-pi=10(+) band has been established up to spin (24(+)) and its crossing with the ground-state band has been studied. In addition, intrinsic high-K states have been identified and on top of two of them, K-pi=7(-) and K-pi=10(-), regular bands have been observed. The K-pi=16(+) and K-pi=18(+) states are yrast whereas the K-pi=14(+) level lies only 33 keV above the yrast line and decays with a low reduced hindrance of f(nu)< 1.3 to the ground-state band (Delta K=14). The results are discussed by means of a systematic comparison with the even-even neighboring nucleus Os-186. Configuration-constrained multiquasiparticle potential-energy-surface calculations have been performed to identify the configurations of multiquasiparticle states.